Chapter 1: Q46P (page 11)

A unit of area often used in measuring land areas is the hectare, defined as $10^{4} m^{2}$ . An open-pit coal mine consumes $75$ hectares of land, down to a depth of $26 m$ , each year. What volume of earth, in cubic kilometers, is removed in this time?

Short Answer

Expert verified

The volume of earth removed is $0.020 {km}^{3}$ .

Step by step solution

Given data

Area of land, $A = 75 h e c t a r e s$

Depth, $d = 26 m$

Understanding the concept of volume

The volume of the earth removed is equal to the product of area and depth. Use the conversion of hectares into square meters and square meters into square kilometers, to find the volume of earth removed.

The expression for volume is given as:

$V = A \times d$ … (i)

Here, A is the area and d is the depth.

Determination of the volume

The conversion factors are as follows:

$1 hectare = 10^{4} m^{2} 1 m^{2} = 10^{- 6} {km}^{2}$

Using equation (i), the volume of earth removed is calculated as:

$V = A \times d = (75 \times 10^{4} m^{2}) \times (26 m) = 1.95 \times 10^{7} m^{3}$

Convert the volume fromto.

$V = (1.95 \times 10^{7} m^{3}) {(\frac{1 km}{1000 m})}^{3} \approx 0.020 {km}^{3}$

Thus, the volume of earth removed is $0.020 {km}^{3}$ .

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A unit of area often used in measuring land areas is the hectare, defined as $10^{4} m^{2}$ . An open-pit coal mine consumes $75$ hectares of land, down to a depth of $26 m$ , each year. What volume of earth, in cubic kilometers, is removed in this time?

Short Answer

Step by step solution

Given data

Understanding the concept of volume

Determination of the volume

One App. One Place for Learning.

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A unit of area often used in measuring land areas is the hectare, defined as104m2. An open-pit coal mine consumes75hectares of land, down to a depth of 26m, each year. What volume of earth, in cubic kilometers, is removed in this time?

Short Answer

Step by step solution

Given data

Understanding the concept of volume

Determination of the volume

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Further Mechanics and Thermal Physics

Physics of Motion

Physical Quantities And Units

Electricity and Magnetism

Measurements

Study anywhere. Anytime. Across all devices.

A unit of area often used in measuring land areas is the hectare, defined as $10^{4} m^{2}$ . An open-pit coal mine consumes $75$ hectares of land, down to a depth of $26 m$ , each year. What volume of earth, in cubic kilometers, is removed in this time?